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C₂×#61871 #10578268

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

6228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

(1,2);(3,4)(5,11)(6,9)(7,10)(8,13)(12,17)(14,16)(15,18)(19,20,23,28)(21,30,32,25)(22,29,24,27)(26,33,34,31);(3,5,7,13)(4,8,10,11)(6,14,15,12)(9,17,18,16)(19,21)(20,25)(22,33)(23,32)(24,31)(26,29)(27,34)(28,30);(19,21)(20,26)(22,31)(23,32)(24,33)(25,29)(27,30)(28,34);(3,6,7,15)(4,9,10,18)(5,12,13,14)(8,16,11,17);(4,10)(8,11)(9,18)(16,17)(19,22,23,24)(20,27,28,29)(21,31,32,33)(25,26,30,34)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10485464);